From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 9 Dec 2020 01:53:03 +0000 (-0500)
Subject: eja: construct fewer temporary matrices during EJA construction.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=commitdiff_plain;h=3f1bc1ad064d41c956b9034edb950e6dbd8eb585

eja: construct fewer temporary matrices during EJA construction.
---

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 83ec50e..5910221 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -1877,7 +1877,6 @@ class ComplexHermitianEJA(ConcreteEJA, ComplexMatrixEJA):
 
             sage: set_random_seed()
             sage: n = ZZ.random_element(1,5)
-            sage: field = QuadraticField(2, 'sqrt2')
             sage: B = ComplexHermitianEJA._denormalized_basis(n)
             sage: all( M.is_symmetric() for M in  B)
             True
@@ -1895,18 +1894,27 @@ class ComplexHermitianEJA(ConcreteEJA, ComplexMatrixEJA):
         #   * The diagonal will (as a result) be real.
         #
         S = []
+        Eij = matrix.zero(F,n)
         for i in range(n):
             for j in range(i+1):
-                Eij = matrix(F, n, lambda k,l: k==i and l==j)
+                # "build" E_ij
+                Eij[i,j] = 1
                 if i == j:
                     Sij = cls.real_embed(Eij)
                     S.append(Sij)
                 else:
                     # The second one has a minus because it's conjugated.
-                    Sij_real = cls.real_embed(Eij + Eij.transpose())
+                    Eij[j,i] = 1 # Eij = Eij + Eij.transpose()
+                    Sij_real = cls.real_embed(Eij)
                     S.append(Sij_real)
-                    Sij_imag = cls.real_embed(I*Eij - I*Eij.transpose())
+                    # Eij = I*Eij - I*Eij.transpose()
+                    Eij[i,j] = I
+                    Eij[j,i] = -I
+                    Sij_imag = cls.real_embed(Eij)
                     S.append(Sij_imag)
+                    Eij[j,i] = 0
+                # "erase" E_ij
+                Eij[i,j] = 0
 
         # Since we embedded these, we can drop back to the "field" that we
         # started with instead of the complex extension "F".
@@ -2162,23 +2170,39 @@ class QuaternionHermitianEJA(ConcreteEJA, QuaternionMatrixEJA):
         #   * The diagonal will (as a result) be real.
         #
         S = []
+        Eij = matrix.zero(Q,n)
         for i in range(n):
             for j in range(i+1):
-                Eij = matrix(Q, n, lambda k,l: k==i and l==j)
+                # "build" E_ij
+                Eij[i,j] = 1
                 if i == j:
                     Sij = cls.real_embed(Eij)
                     S.append(Sij)
                 else:
                     # The second, third, and fourth ones have a minus
                     # because they're conjugated.
-                    Sij_real = cls.real_embed(Eij + Eij.transpose())
+                    # Eij = Eij + Eij.transpose()
+                    Eij[j,i] = 1
+                    Sij_real = cls.real_embed(Eij)
                     S.append(Sij_real)
-                    Sij_I = cls.real_embed(I*Eij - I*Eij.transpose())
+                    # Eij = I*(Eij - Eij.transpose())
+                    Eij[i,j] = I
+                    Eij[j,i] = -I
+                    Sij_I = cls.real_embed(Eij)
                     S.append(Sij_I)
-                    Sij_J = cls.real_embed(J*Eij - J*Eij.transpose())
+                    # Eij = J*(Eij - Eij.transpose())
+                    Eij[i,j] = J
+                    Eij[j,i] = -J
+                    Sij_J = cls.real_embed(Eij)
                     S.append(Sij_J)
-                    Sij_K = cls.real_embed(K*Eij - K*Eij.transpose())
+                    # Eij = K*(Eij - Eij.transpose())
+                    Eij[i,j] = K
+                    Eij[j,i] = -K
+                    Sij_K = cls.real_embed(Eij)
                     S.append(Sij_K)
+                    Eij[j,i] = 0
+                # "erase" E_ij
+                Eij[i,j] = 0
 
         # Since we embedded these, we can drop back to the "field" that we
         # started with instead of the quaternion algebra "Q".